Water enters a pipe system at point 1. The pipe system drops 100 m and then enco

Question

Water enters a pipe system at point 1. The pipe system drops 100 m and then encounters a constriction/expansion in the pipe at point 2, and ultimately exits the pipe system at point 3. Assume    1) the density of the water is constant at 1 g/cm^3 2) There is no loss of energy to friction 3) There is no loss of energy at the constriction/expansion (point 2) 4) the flow is laminar and irrotational.
The known pressures, heights, velocities, and radii of the pipe at points 1, 2 and 3 are included in the diagram below. What is the velocity of the water at point 3? Show your detailed work! 202, 650 Pa P height 100 m velocity 5 m/s radius 10 m P 101, 325 Pa height- 0 m (2 velocity. m/s radius m P 202, 650 Pa height 100 m velocity sm/s radius 10 m

Explanation / Answer

Hi,

Please find the below solution.

As per bernoulli's equation.

P1+ 0.5 pV12+ pgH1 = P2+ 0.5 pV22+ pgH2

202650 + 0.5 *1000*5*5 + 1000*9.81.*100 = 101325 + 0.5*1000*V22 + 1000*9.81.*0

V2=6.8m/sec

P2+ 0.5 pV22+ pgH2 = P3+ 0.5 pV32+ pgH3

101325 + 0.5*1000*6.82 + 1000*9.81.*0 = 202650 + 0.5 *1000*V32 + 1000*9.81.*100

V3= 5 m/s

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